This ebook is an advent to combinatorial torsions of mobile areas and manifolds with detailed emphasis on torsions of three-d manifolds. the 1st chapters disguise algebraic foundations of the speculation of torsions and diverse topological buildings of torsions because of ok. Reidemeister, J.H.C. Whitehead, J. Milnor and the writer. We additionally speak about connections among the torsions and the Alexander polynomials of hyperlinks and 3-manifolds. The 3rd (and final) bankruptcy of the ebook bargains with so-called sophisticated torsions and the similar extra buildings on manifolds, in particular homological orientations and Euler buildings. As an software, we supply a development of the multivariable Conway polynomial of hyperlinks in homology 3-spheres. on the finish of the e-book, we in brief describe the new result of G. Meng, C.H. Taubes and the writer at the connections among the sophisticated torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed toward scholars, expert mathematicians and physicists drawn to combinatorial points of topology and/or in low dimensional topology. the mandatory heritage for the reader comprises the easy fundamentals of topology and homological algebra.

In a few recognized works, M. Kac confirmed that quite a few tools of chance conception will be fruitfully utilized to special difficulties of research. The interconnection among chance and research additionally performs a imperative function within the current booklet. despite the fact that, our technique is especially according to the appliance of research equipment (the approach to operator identities, indispensable equations thought, twin platforms, integrable equations) to chance conception (Levy tactics, M.

As soon as the privilege of a mystery few, cryptography is now taught at universities worldwide. advent to Cryptography with Open-Source software program illustrates algorithms and cryptosystems utilizing examples and the open-source machine algebra approach of Sage. the writer, a famous educator within the box, offers a hugely useful studying event through progressing at a gradual speed, conserving arithmetic at a workable point, and together with a number of end-of-chapter workouts.

This booklet constitutes the refereed lawsuits of the tenth foreign convention on Combinatorics on phrases, phrases 2015, held in Kiel, Germany, in September 2015 less than the auspices of the EATCS. The 14 revised complete papers provided have been rigorously reviewed and chosen from 22 submissions. the most item within the contributions are phrases, finite or endless sequences of symbols over a finite alphabet.